Background

This analysis document compliments FIA NLS Models: Biomass Growth vs. Stand Age. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.

Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)

Below the model fitting procedure is implemented by ecoprovince:

Temporally-balancing the biomass growth data set

Lets look at some quick attributes of the dataset

  • The data set has 115221 observations, comprised of 58079 plots.
  • The frequency of growth measurements among plots is as follows (n=1 through 5): 25558, 13784, 12967, 5656, 114.
  • Thus 55.99% of plots have at least two growth measurements.

Analysis 1: Temporally-balanced analysis

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   4826     1878.4                              
## 2   4825     1875.8  1   2.56  6.5836 0.01032 *  
## 3   4790     1374.2 35 501.56 49.9492 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 20213.00
## 2     2 20208.41
## 3     3 18612.85
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.193378   0.191516   1.010   0.3127    
## phi    0.004988   0.005728   0.871   0.3840    
## alpha  0.646138   0.040873  15.809   <2e-16 ***
## a      0.000000   2.576629   0.000   1.0000    
## b      3.455624   2.565245   1.347   0.1780    
## c     31.704020   2.569992  12.336   <2e-16 ***
## d      2.849389   1.291808   2.206   0.0274 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5356 on 4790 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (37 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93396, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.7501, p-value = 9.182e-15
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  10034     3645.4                                  
## 2  10032     3641.5   2    3.88  5.3403  0.004808 ** 
## 3   9747     1913.3 285 1728.23 30.8923 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 43561.12
## 2     2 43549.03
## 3     3 36432.77
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.315750   0.233404   5.637 1.78e-08 ***
## phi    0.019104   0.004506   4.240 2.26e-05 ***
## alpha  0.731615   0.028779  25.422  < 2e-16 ***
## a      0.822273   0.198416   4.144 3.44e-05 ***
## b      1.593947   0.195682   8.146 4.24e-16 ***
## c     22.040911   0.662612  33.264  < 2e-16 ***
## d      2.050107   0.202484  10.125  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4431 on 9747 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3222 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5452     2464.1                                
## 2   5451     2458.8  1   5.31  11.769 0.0006067 ***
## 3   5415     2051.7 36 407.05  29.842 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25174.05
## 2     2 25164.28
## 3     3 24063.35
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.646969   0.155884  -4.150 3.37e-05 ***
## phi    0.016955   0.006576   2.578  0.00995 ** 
## alpha  0.722879   0.047031  15.370  < 2e-16 ***
## a      0.000000   3.912967   0.000  1.00000    
## b      4.533953   3.910372   1.159  0.24632    
## c     35.586426   3.534938  10.067  < 2e-16 ***
## d      3.089853   1.630066   1.896  0.05807 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6155 on 5415 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (40 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   2854     1139.3                              
## 2   2853     1139.1   1   0.22  0.5552 0.4563    
## 3   2734      451.6 119 687.54 34.9781 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14497.96
## 2     2 14499.40
## 3     3 11523.33
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.13938    0.29951  -0.465 0.641717    
## phi    0.03301    0.01306   2.527 0.011555 *  
## alpha  0.79429    0.05883  13.502  < 2e-16 ***
## a      1.80705    0.45900   3.937 8.46e-05 ***
## b      1.62062    0.45288   3.578 0.000352 ***
## c     45.67005    4.60883   9.909  < 2e-16 ***
## d      1.86961    0.46428   4.027 5.81e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4064 on 2734 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (813 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92559, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.6967, p-value = 1.397e-14
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Error in nls(fg2_2, data = G_223, start = c(ge = ge.start, a = a.start,  : 
##   parameters without starting value in 'data': phi
##   model      AIC
## 1     1 25409.44
## 2     2       NA
## 3     3 22477.46
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.797118   0.151000  -5.279 1.35e-07 ***
## phi    0.000000   0.008996   0.000  1.00000    
## alpha  0.603323   0.052645  11.460  < 2e-16 ***
## a      2.773083   0.618182   4.486 7.42e-06 ***
## b      1.563226   0.598919   2.610  0.00908 ** 
## c     28.777834   2.742419  10.494  < 2e-16 ***
## d      1.369724   0.451733   3.032  0.00244 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4961 on 5256 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1127 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)    
## 1   8153     4439.7                               
## 2   8152     4437.3   1   2.41  4.4243 0.03546 *  
## 3   8030     3869.9 122 567.36  9.6496 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42664.17
## 2     2 42661.74
## 3     3 41126.27
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.774532   0.181640   4.264 2.03e-05 ***
## phi    0.007915   0.005876   1.347    0.178    
## alpha  0.886658   0.028291  31.341  < 2e-16 ***
## a      2.364704   0.286628   8.250  < 2e-16 ***
## b      3.197970   0.279054  11.460  < 2e-16 ***
## c     18.756519   0.555395  33.771  < 2e-16 ***
## d      1.467666   0.125366  11.707  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6942 on 8030 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (163 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 20 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   8129     5671.1                                 
## 2   8128     5663.5   1    7.6  10.905  0.000963 ***
## 3   7970     4983.5 158  680.0   6.883 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42533.94
## 2     2 42525.04
## 3     3 40898.07
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.957099   0.223185   4.288 1.82e-05 ***
## phi    0.011836   0.006192   1.911    0.056 .  
## alpha  0.872885   0.028880  30.225  < 2e-16 ***
## a      3.120769   0.145123  21.504  < 2e-16 ***
## b      2.073713   0.136788  15.160  < 2e-16 ***
## c     16.362762   0.622097  26.303  < 2e-16 ***
## d      0.889109   0.070091  12.685  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7907 on 7970 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (217 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    846     572.27                                
## 2    845     572.06  1  0.214  0.3167    0.5737    
## 3    825     521.15 20 50.910  4.0296 9.517e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4519.781
## 2     2 4521.463
## 3     3 4375.857
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.446255   1.303516   1.110 0.267536    
## phi    0.000823   0.027595   0.030 0.976214    
## alpha  0.857648   0.104810   8.183 1.05e-15 ***
## a      3.267454   0.709421   4.606 4.76e-06 ***
## b      1.978059   0.689381   2.869 0.004219 ** 
## c     18.907883   2.683055   7.047 3.86e-12 ***
## d      0.660469   0.199429   3.312 0.000967 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7948 on 825 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (30 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits ### plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8819, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.0363, p-value = 5.43e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1038     516.93                             
## 2   1037     516.93  1   0.00    0.00      1    
## 3    975     194.87 62 322.06   25.99 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5430.578
## 2     2 5432.578
## 3     3 4229.322
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge     0.21188    0.64841   0.327  0.74392   
## phi    0.00000    0.01848   0.000  1.00000   
## alpha  0.43219    0.15080   2.866  0.00425 **
## a      0.00000   87.40235   0.000  1.00000   
## b      2.97494   87.33232   0.034  0.97283   
## c     14.41230   20.09081   0.717  0.47333   
## d      5.62159   90.43132   0.062  0.95044   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4471 on 975 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (412 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.73795, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.0562, p-value = 0.03977
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    440     887.59                              
## 2    439     867.17  1 20.423  10.339 0.001399 **
## 3    415     838.84 24 28.329   0.584 0.943282   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2424.892
## 2     2 2416.533
## 3     3 2319.289
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.69353    1.70607   0.407  0.68458    
## phi    0.17568    0.06137   2.863  0.00441 ** 
## alpha  0.14853    0.42346   0.351  0.72595    
## a      0.76884    0.67928   1.132  0.25835    
## b      2.17686    0.96905   2.246  0.02520 *  
## c     18.12283    3.84593   4.712 3.35e-06 ***
## d      1.15102    0.50348   2.286  0.02275 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.422 on 415 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9665, p-value = 3.081e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.4823, p-value = 0.0004972
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5098     1399.0                                
## 2   5097     1390.7  1  8.260  30.275 3.933e-08 ***
## 3   5082     1308.7 15 82.042  21.240 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19322.30
## 2     2 19294.08
## 3     3 18948.50
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.940633   0.236326   3.980 6.98e-05 ***
## phi    0.022656   0.005238   4.325 1.55e-05 ***
## alpha  0.625087   0.034889  17.917  < 2e-16 ***
## a      2.239747   0.250448   8.943  < 2e-16 ***
## b      0.747572   0.210668   3.549 0.000391 ***
## c     30.670631   2.600559  11.794  < 2e-16 ***
## d      1.163150   0.344947   3.372 0.000752 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5075 on 5082 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   5256     3349.7                             
## 2   5255     3349.7  1   0.00   0.000      1    
## 3   5227     3020.7 28 329.07  20.337 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 26437.59
## 2     2 26439.59
## 3     3 25793.14
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.256839   0.238504   1.077 0.281585    
## phi    0.000000   0.008957   0.000 1.000000    
## alpha  0.848303   0.072050  11.774  < 2e-16 ***
## a      2.573482   0.550708   4.673 3.04e-06 ***
## b      1.947714   0.502195   3.878 0.000106 ***
## c     28.680202   2.460324  11.657  < 2e-16 ***
## d      1.303224   0.344685   3.781 0.000158 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7602 on 5227 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (28 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    598     363.57                                
## 2    597     363.56  1  0.010  0.0164 0.8982009    
## 3    593     349.87  4 13.682  5.7972 0.0001398 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2558.886
## 2     2 2560.869
## 3     3 2530.660
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.29175    2.05903   1.599 0.110422    
## phi    0.00000    0.03284   0.000 1.000000    
## alpha  0.97478    0.20513   4.752 2.53e-06 ***
## a      1.48977    0.38262   3.894 0.000110 ***
## b      1.21350    0.46832   2.591 0.009801 ** 
## c     30.79223    2.73735  11.249  < 2e-16 ***
## d      0.40889    0.10901   3.751 0.000193 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7681 on 593 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94973, p-value = 2.048e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.9525, p-value = 0.05088
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(fg2_3, data = G_M231, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    672     378.26                                
## 2    671     368.21  1 10.055  18.324 2.135e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2897.814
## 2     2 2881.574
## 3     3       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   2.50558    1.89775   1.320 0.187188    
## phi  0.10690    0.03246   3.293 0.001043 ** 
## a    1.59568    0.41897   3.809 0.000153 ***
## b    2.61731    1.09677   2.386 0.017292 *  
## c    8.32447    0.36083  23.070  < 2e-16 ***
## d    0.14000    0.04573   3.062 0.002289 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7408 on 671 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95405, p-value = 1.085e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.0879, p-value = 3.621e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_M242, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_2, data = G_M242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_3, data = G_M242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value  Pr(>F)  
## 1    164     4.2484                              
## 2    163     4.1772  1 0.071264  2.7809 0.09732 .
## 3    162     4.0932  1 0.083971  3.3234 0.07014 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 651.0310
## 2     2 650.1721
## 3     3 648.7402
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.40380    1.18751  -2.024 0.044589 *  
## phi    0.11429    0.06088   1.877 0.062290 .  
## alpha  0.63487    0.29797   2.131 0.034624 *  
## a      2.65500    1.78504   1.487 0.138863    
## b      6.74457    4.26227   1.582 0.115511    
## c     43.36414    5.98332   7.248 1.64e-11 ***
## d      0.69853    0.17766   3.932 0.000125 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.159 on 162 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (171 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93958, p-value = 1.415e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.6143, p-value = 0.1065
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1    218     35.122                             
## 2    217     35.122  1  0.000   0.000 0.9994    
## 3    211     21.490  6 13.632  22.308 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 891.5661
## 2     2 893.5661
## 3     3 774.9166
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.51871    1.78829  -0.290 0.772055    
## phi    0.00000    0.04936   0.000 1.000000    
## alpha  0.82065    0.20888   3.929 0.000116 ***
## a      0.00000    4.66310   0.000 1.000000    
## b      1.92469    4.69391   0.410 0.682193    
## c     59.02216    9.54875   6.181 3.24e-09 ***
## d      1.38505    2.26567   0.611 0.541645    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3191 on 211 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (92 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.80029, p-value = 5.396e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.89306, p-value = 0.3718
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest 3
222 Midwest Broadleaf Forest 3
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) 3
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4834 2417 0.1933784 0.0366785 -0.1820813 0.5688382 0.0049875 0.0000328 -0.0062429 0.0162180 0.6461380 0.0016706 0.5660087 0.7262673 0.0000000 -5.0513757 5.051376 3.4556239 -1.5734339 8.484682 31.704020 26.665654 36.742385 2.8493889 0.3168514 5.3819264
212 Laurentian Mixed Forest east 12976 6488 1.3157502 0.0544772 0.8582309 1.7732694 0.0191040 0.0000203 0.0102712 0.0279367 0.7316154 0.0008282 0.6752022 0.7880285 0.8222733 0.4333372 1.211210 1.5939474 1.2103701 1.977525 22.040911 20.742054 23.339768 2.0501066 1.6531954 2.4470177
221 Eastern Broadleaf Forest east 5462 2731 -0.6469689 0.0242999 -0.9525644 -0.3413734 0.0169548 0.0000432 0.0040638 0.0298457 0.7228794 0.0022119 0.6306803 0.8150785 0.0000000 -7.6709889 7.670989 4.5339529 -3.1319484 12.199854 35.586426 28.656526 42.516325 3.0898533 -0.1057315 6.2854381
222 Midwest Broadleaf Forest east 3554 1777 -0.1393791 0.0897082 -0.7266744 0.4479162 0.0330114 0.0001706 0.0073976 0.0586251 0.7942885 0.0034605 0.6789413 0.9096358 1.8070512 0.9070230 2.707079 1.6206198 0.7326025 2.508637 45.670049 36.632901 54.707197 1.8696060 0.9592353 2.7799766
223 Central Interior Broadleaf Forest east 6390 3195 -0.7971176 0.0228011 -1.0931413 -0.5010940 0.0000000 0.0000809 -0.0176361 0.0176361 0.6033233 0.0027715 0.5001176 0.7065291 2.7730826 1.5611891 3.984976 1.5632260 0.3890954 2.737357 28.777834 23.401553 34.154116 1.3697238 0.4841395 2.2553080
231 Southeastern Mixed Forest east 8200 4100 0.7745322 0.0329929 0.4184716 1.1305928 0.0079151 0.0000345 -0.0036026 0.0194328 0.8866583 0.0008004 0.8312008 0.9421157 2.3647040 1.8028389 2.926569 3.1979701 2.6509527 3.744987 18.756519 17.667800 19.845237 1.4676664 1.2219158 1.7134170
232 Outer Coastal Plain Mixed Forest east 8194 4097 0.9570986 0.0498115 0.5195980 1.3945993 0.0118356 0.0000383 -0.0003022 0.0239733 0.8728854 0.0008340 0.8162737 0.9294972 3.1207692 2.8362895 3.405249 2.0737128 1.8055724 2.341853 16.362762 15.143289 17.582235 0.8891088 0.7517122 1.0265053
234 Lower Mississippi Riverine Forest east 862 431 1.4462552 1.6991535 -1.1123425 4.0048529 0.0008230 0.0007615 -0.0533425 0.0549885 0.8576484 0.0109851 0.6519227 1.0633741 3.2674540 1.8749715 4.659936 1.9780593 0.6249119 3.331207 18.907883 13.641466 24.174300 0.6604686 0.2690210 1.0519163
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1394 697 0.2118765 0.4204376 -1.0605665 1.4843194 0.0000000 0.0003415 -0.0362643 0.0362643 0.4321891 0.0227421 0.1362495 0.7281286 0.0000000 -171.5183718 171.518372 2.9749371 -168.4060055 174.355880 14.412295 -25.013915 53.838505 5.6215915 -171.8408436 183.0840266
255 Prairie Parkland (Subtropical) east 446 223 0.6935298 2.9106676 -2.6600823 4.0471419 0.1756790 0.0037663 0.0550435 0.2963144 0.1485288 0.1793183 -0.6838649 0.9809225 0.7688379 -0.5664169 2.104093 2.1768590 0.2720068 4.081711 18.122829 10.562891 25.682767 1.1510239 0.1613315 2.1407163
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5104 2552 0.9406330 0.0558499 0.4773325 1.4039335 0.0226561 0.0000274 0.0123873 0.0329249 0.6250871 0.0012172 0.5566902 0.6934840 2.2397473 1.7487612 2.730733 0.7475724 0.3345724 1.160572 30.670631 25.572414 35.768848 1.1631498 0.4869044 1.8393951
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5262 2631 0.2568394 0.0568842 -0.2107285 0.7244073 0.0000000 0.0000802 -0.0175596 0.0175596 0.8483035 0.0051911 0.7070563 0.9895506 2.5734825 1.4938646 3.653100 1.9477135 0.9632021 2.932225 28.680202 23.856938 33.503466 1.3032238 0.6274974 1.9789501
M223 Ozark Broadleaf Forest Meadow east 604 302 3.2917489 4.2395904 -0.7521226 7.3356205 0.0000000 0.0010788 -0.0645063 0.0645063 0.9747756 0.0420796 0.5719000 1.3776512 1.4897731 0.7383163 2.241230 1.2135029 0.2937271 2.133279 30.792233 25.416156 36.168310 0.4088893 0.1947995 0.6229792
M231 Ouachita Mixed Forest east 678 339 2.5055787 3.6014372 -1.2206550 6.2318123 0.1069028 0.0010539 0.0431601 0.1706455 NA NA NA NA 1.5956826 0.7730305 2.418335 2.6173145 0.4637910 4.770838 8.324472 7.615972 9.032971 0.1400017 0.0502173 0.2297860
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 340 170 -2.4038014 1.4101854 -4.7488006 -0.0588022 0.1142913 0.0037069 -0.0059378 0.2345204 0.6348730 0.0887841 0.0464738 1.2232722 2.6550045 -0.8699451 6.179954 6.7445655 -1.6722040 15.161335 43.364143 31.548785 55.179500 0.6985345 0.3477068 1.0493621
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 310 155 -0.5187127 3.1979869 -4.0439195 3.0064940 0.0000000 0.0024368 -0.0973102 0.0973102 0.8206473 0.0436301 0.4088918 1.2324027 0.0000000 -9.1922342 9.192234 1.9246863 -7.3282724 11.177645 59.022159 40.198997 77.845321 1.3850538 -3.0812017 5.8513094
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 20 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 20 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 21 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 21 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region  weighted.ge weighted.ge.std_Error 95 % CI, upper
## 1     entire US  0.519535745           0.080980585   0.6782576920
## 2       pacific -0.012565611           0.006207592  -0.0003987315
## 3          east  0.534573619           0.080291188   0.6919443480
## 4 interior west -0.002472263           0.008523268   0.0142333421
##   95 % CI, lower
## 1     0.36081380
## 2    -0.02473249
## 3     0.37720289
## 4    -0.01917787

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US 0.0146037098           0.0022952268   0.0191023544
## 2       pacific 0.0005974453           0.0003182659   0.0012212465
## 3          east 0.0140062644           0.0022608445   0.0184375196
## 4 interior west 0.0000000000           0.0002352772   0.0004611432
##   95 % CI, lower
## 1   1.010507e-02
## 2  -2.635576e-05
## 3   9.575009e-03
## 4  -4.611432e-04

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.734719810             0.0137897212    0.761747663
## 2       pacific    0.003318730             0.0015575878    0.006371602
## 3          east    0.727489751             0.0136652560    0.754273653
## 4 interior west    0.003911329             0.0009955451    0.005862597
##   95 % CI, lower
## 1   0.7076919565
## 2   0.0002658578
## 3   0.7007058496
## 4   0.0019600606

Analysis 2: Temporally-balanced, No-harvest

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3752     1425.7                             
## 2   3751     1424.8  1   0.85  2.2493 0.1338    
## 3   3719     1102.3 32 322.50 34.0013 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15719.00
## 2     2 15718.75
## 3     3 14669.80
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.225077   0.224240   1.004    0.316    
## phi    0.003788   0.006570   0.577    0.564    
## alpha  0.710688   0.088408   8.039 1.21e-15 ***
## a      0.000000   3.906624   0.000    1.000    
## b      3.416812   3.887564   0.879    0.380    
## c     30.345394   2.966165  10.231  < 2e-16 ***
## d      2.920245   1.991604   1.466    0.143    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5444 on 3719 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (34 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92666, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.0029, p-value = 2.507e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)    
## 1   8121     2830.5                               
## 2   8119     2827.5   2    3.0  4.3049 0.01353 *  
## 3   7863     1594.0 256 1233.5 23.7684 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 34848.85
## 2     2 34838.85
## 3     3 29572.19
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.073352   0.243939   4.400 1.10e-05 ***
## phi    0.016990   0.005101   3.331 0.000871 ***
## alpha  0.576091   0.049898  11.545  < 2e-16 ***
## a      0.936434   0.201091   4.657 3.26e-06 ***
## b      1.504802   0.194661   7.730 1.20e-14 ***
## c     22.200089   0.815840  27.211  < 2e-16 ***
## d      1.905112   0.207828   9.167  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4502 on 7863 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2612 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 21 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   4467     1979.1                                 
## 2   4466     1976.0  1   3.114   7.037  0.008012 ** 
## 3   4433     1730.7 33 245.343  19.044 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 20675.28
## 2     2 20670.24
## 3     3 19973.85
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.646589   0.175698  -3.680 0.000236 ***
## phi    0.016471   0.007435   2.215 0.026789 *  
## alpha  0.688822   0.085486   8.058 9.91e-16 ***
## a      0.000000   3.641690   0.000 1.000000    
## b      4.525004   3.638859   1.244 0.213741    
## c     35.492113   3.519003  10.086  < 2e-16 ***
## d      2.935701   1.455958   2.016 0.043825 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6248 on 4433 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88597, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.381, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   2250     930.63                              
## 2   2249     930.48   1   0.15  0.3619 0.5475    
## 3   2136     363.61 113 566.87 29.4691 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 11488.094
## 2     2 11489.731
## 3     3  9056.514
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.25657    0.32601  -0.787 0.431373    
## phi    0.02804    0.01469   1.909 0.056342 .  
## alpha  0.76351    0.08885   8.594  < 2e-16 ***
## a      2.04022    0.41787   4.882 1.13e-06 ***
## b      1.39677    0.40873   3.417 0.000644 ***
## c     48.40263    5.47352   8.843  < 2e-16 ***
## d      1.62332    0.45453   3.571 0.000363 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4126 on 2136 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (655 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93933, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.8368, p-value = 4.621e-15
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Error in nls(fg2_2, data = G_223, start = c(ge = ge.start, a = a.start,  : 
##   parameters without starting value in 'data': phi
##   model      AIC
## 1     1 20999.77
## 2     2       NA
## 3     3 18427.20
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.85404    0.16575  -5.153 2.69e-07 ***
## phi    0.00000    0.01008   0.000  1.00000    
## alpha  0.50058    0.09405   5.322 1.08e-07 ***
## a      2.84500    0.51862   5.486 4.36e-08 ***
## b      1.48126    0.50082   2.958  0.00312 ** 
## c     30.63534    2.85138  10.744  < 2e-16 ***
## d      1.23205    0.37968   3.245  0.00118 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4994 on 4267 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (848 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)    
## 1   6402     3141.1                               
## 2   6401     3140.6   1   0.491  1.0004 0.3173    
## 3   6291     2932.9 110 207.626  4.0486 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33390.23
## 2     2 33391.23
## 3     3 32584.79
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.679888   0.200724   3.387  0.00071 ***
## phi    0.008068   0.006643   1.214  0.22463    
## alpha  0.766437   0.072229  10.611  < 2e-16 ***
## a      1.844170   0.393290   4.689  2.8e-06 ***
## b      3.612811   0.391088   9.238  < 2e-16 ***
## c     19.509386   0.623461  31.292  < 2e-16 ***
## d      1.668083   0.161068  10.356  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6828 on 6291 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (146 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 15 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value  Pr(>F)    
## 1   6478     4130.0                                
## 2   6477     4127.9   1   2.104  3.3010 0.06929 .  
## 3   6349     3890.9 128 236.974  3.0209 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33938.10
## 2     2 33936.79
## 3     3 33074.28
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.048845   0.265513   3.950 7.89e-05 ***
## phi    0.006725   0.007023   0.958    0.338    
## alpha  0.721818   0.061190  11.796  < 2e-16 ***
## a      3.004204   0.164092  18.308  < 2e-16 ***
## b      1.947009   0.150801  12.911  < 2e-16 ***
## c     16.907229   0.753991  22.424  < 2e-16 ***
## d      0.908464   0.085197  10.663  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7828 on 6349 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (184 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 31 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    701     435.21                                
## 2    700     435.13  1  0.081  0.1303 0.7182252    
## 3    680     406.44 20 28.681  2.3993 0.0005911 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3724.973
## 2     2 3726.842
## 3     3 3614.833
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.10947    1.25666   0.883  0.37761    
## phi    0.00000    0.02986   0.000  1.00000    
## alpha  0.81627    0.17317   4.714 2.95e-06 ***
## a      3.24768    0.74265   4.373 1.42e-05 ***
## b      1.91997    0.65980   2.910  0.00373 ** 
## c     21.38038    3.64236   5.870 6.81e-09 ***
## d      0.70116    0.25066   2.797  0.00530 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7731 on 680 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits ### plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.902, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.9476, p-value = 0.003203
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1    924     488.51                             
## 2    923     488.51  1   0.00   0.000      1    
## 3    864     182.65 59 305.87  24.523 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4877.980
## 2     2 4879.980
## 3     3 3786.144
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge      0.29503    0.73064   0.404   0.6865  
## phi     0.00000    0.01979   0.000   1.0000  
## alpha   0.42949    0.19039   2.256   0.0243 *
## a       0.00000  253.81733   0.000   1.0000  
## b       2.84800  253.71862   0.011   0.9910  
## c      11.23783   33.74535   0.333   0.7392  
## d       7.80526  367.62748   0.021   0.9831  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4598 on 864 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (349 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.72826, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.3062, p-value = 0.0009458
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    408     1147.6                              
## 2    407     1123.7  1 23.880  8.6491 0.003459 **
## 3    383     1084.0 24 39.738  0.5850 0.942436   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2378.960
## 2     2 2372.275
## 3     3 2273.031
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.58436    4.80697   0.746   0.4563    
## phi    0.19284    0.08137   2.370   0.0183 *  
## alpha  0.21593    0.61601   0.351   0.7261    
## a      0.00000    1.11339   0.000   1.0000    
## b      1.94993    1.53323   1.272   0.2042    
## c     14.89018    2.27209   6.554 1.82e-10 ***
## d      1.57113    0.89316   1.759   0.0794 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.682 on 383 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96949, p-value = 2.811e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.7178, p-value = 0.000201
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   3960     965.64                                 
## 2   3959     962.49  1  3.1497 12.9556 0.0003229 ***
## 3   3945     946.55 14 15.9474  4.7475 1.009e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14718.66
## 2     2 14707.70
## 3     3 14609.22
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.186426   0.286790   4.137 3.59e-05 ***
## phi    0.021283   0.005786   3.678 0.000238 ***
## alpha  0.460344   0.086347   5.331 1.03e-07 ***
## a      2.184626   0.213334  10.240  < 2e-16 ***
## b      0.646730   0.161405   4.007 6.27e-05 ***
## c     29.329397   2.872077  10.212  < 2e-16 ***
## d      1.089173   0.329610   3.304 0.000960 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 3945 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98312, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.5409, p-value = 4.666e-14
## alternative hypothesis: two.sided

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   4682     2980.7                             
## 2   4681     2980.7  1    0.0   0.000      1    
## 3   4654     2695.9 27  284.8  18.209 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23616.45
## 2     2 23618.45
## 3     3 23048.87
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.243551   0.251964   0.967 0.333789    
## phi    0.000000   0.009489   0.000 1.000000    
## alpha  0.897981   0.118962   7.548 5.27e-14 ***
## a      2.612340   0.554196   4.714 2.50e-06 ***
## b      1.898612   0.498966   3.805 0.000144 ***
## c     28.445897   2.601549  10.934  < 2e-16 ***
## d      1.279176   0.356674   3.586 0.000339 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7611 on 4654 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86793, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.5443, p-value = 5.976e-11
## alternative hypothesis: two.sided

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    524     311.92                            
## 2    523     311.92  1 0.0002  0.0003 0.98587  
## 3    519     306.31  4 5.6074  2.3752 0.05114 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2253.534
## 2     2 2255.533
## 3     3 2239.595
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge      2.7321     1.9279   1.417 0.157051    
## phi     0.0000     0.0354   0.000 1.000000    
## alpha   0.7405     0.3428   2.160 0.031217 *  
## a       1.5518     0.4098   3.786 0.000171 ***
## b       1.1397     0.4550   2.505 0.012550 *  
## c      31.3444     3.2501   9.644  < 2e-16 ***
## d       0.4420     0.1369   3.229 0.001321 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7682 on 519 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94481, p-value = 4.385e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.8213, p-value = 0.06856
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_M231, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_2, data = G_M231, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_3, data = G_M231, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    672     378.26                                
## 2    671     368.21  1 10.055  18.324 2.135e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2897.814
## 2     2 2881.574
## 3     3       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   2.50558    1.89775   1.320 0.187188    
## phi  0.10690    0.03246   3.293 0.001043 ** 
## a    1.59568    0.41897   3.809 0.000153 ***
## b    2.61731    1.09677   2.386 0.017292 *  
## c    8.32447    0.36083  23.070  < 2e-16 ***
## d    0.14000    0.04573   3.062 0.002289 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7408 on 671 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95405, p-value = 1.085e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.0879, p-value = 3.621e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_M242, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_2, data = G_M242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_3, data = G_M242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value  Pr(>F)  
## 1    155     3.8918                              
## 2    154     3.7881  1 0.103657  4.2140 0.04178 *
## 3    153     3.7187  1 0.069373  2.8542 0.09317 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 609.8531
## 2     2 607.5337
## 3     3 606.5764
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.37395    1.26971  -1.870 0.063439 .  
## phi    0.14571    0.05622   2.592 0.010476 *  
## alpha  0.63651    0.32009   1.989 0.048537 *  
## a      2.98472    2.02026   1.477 0.141625    
## b      6.78463    4.47605   1.516 0.131642    
## c     41.94215    6.16319   6.805 2.15e-10 ***
## d      0.66258    0.17696   3.744 0.000256 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1559 on 153 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (162 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94206, p-value = 3.972e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.61669, p-value = 0.5374
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    181     52.155                                
## 2    180     52.155  1  0.000  0.0000         1    
## 3    174     39.478  6 12.677  9.3126 7.463e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 809.9020
## 2     2 811.9020
## 3     3 746.8285
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.84468    0.40013  -7.109 2.89e-11 ***
## phi    0.06435    0.04798   1.341  0.18157    
## alpha  1.07237    0.35853   2.991  0.00318 ** 
## a      0.00000   15.87378   0.000  1.00000    
## b      4.06202   15.63642   0.260  0.79534    
## c     67.09623   16.12712   4.160 4.98e-05 ***
## d      1.37153    3.64708   0.376  0.70733    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4763 on 174 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (77 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.83503, p-value = 4.863e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.96554, p-value = 0.3343
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (geom_point).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest 3
222 Midwest Broadleaf Forest 3
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) 3
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4834 2417 0.2250766 0.0502837 -0.2145693 0.6647226 0.0037875 0.0000432 -0.0090926 0.0166677 0.7106877 0.0078160 0.5373549 0.8840206 0.0000000 -7.6593360 7.659336 3.4168122 -4.2051547 11.0387791 30.345394 24.529925 36.160864 2.9202451 -0.9844974 6.824988
212 Laurentian Mixed Forest east 12976 6488 1.0733519 0.0595063 0.5951663 1.5515375 0.0169898 0.0000260 0.0069903 0.0269893 0.5760909 0.0024898 0.4782773 0.6739044 0.9364341 0.5422423 1.330626 1.5048016 1.1232152 1.8863879 22.200089 20.600826 23.799351 1.9051119 1.4977135 2.312510
221 Eastern Broadleaf Forest east 5462 2731 -0.6465893 0.0308696 -0.9910443 -0.3021343 0.0164707 0.0000553 0.0018946 0.0310468 0.6888216 0.0073079 0.5212256 0.8564177 0.0000000 -7.1395298 7.139530 4.5250041 -2.6089765 11.6589846 35.492113 28.593110 42.391115 2.9357011 0.0812975 5.790105
222 Midwest Broadleaf Forest east 3554 1777 -0.2565694 0.1062837 -0.8959032 0.3827644 0.0280413 0.0002157 -0.0007587 0.0568413 0.7635138 0.0078938 0.5892780 0.9377496 2.0402172 1.2207385 2.859696 1.3967743 0.5952238 2.1983247 48.402626 37.668636 59.136616 1.6233158 0.7319490 2.514683
223 Central Interior Broadleaf Forest east 6390 3195 -0.8540404 0.0274733 -1.1789980 -0.5290829 0.0000000 0.0001016 -0.0197641 0.0197641 0.5005751 0.0088463 0.3161791 0.6849710 2.8450004 1.8282307 3.861770 1.4812635 0.4993934 2.4631337 30.635340 25.045148 36.225532 1.2320518 0.4876882 1.976415
231 Southeastern Mixed Forest east 8200 4100 0.6798877 0.0402901 0.2864004 1.0733749 0.0080677 0.0000441 -0.0049553 0.0210908 0.7664374 0.0052170 0.6248448 0.9080300 1.8441701 1.0731878 2.615152 3.6128114 2.8461464 4.3794765 19.509386 18.287190 20.731581 1.6680829 1.3523338 1.983832
232 Outer Coastal Plain Mixed Forest east 8194 4097 1.0488449 0.0704973 0.5283491 1.5693407 0.0067246 0.0000493 -0.0070429 0.0204921 0.7218179 0.0037443 0.6018640 0.8417717 3.0042044 2.6825286 3.325880 1.9470091 1.6513878 2.2426303 16.907229 15.429153 18.385306 0.9084636 0.7414489 1.075478
234 Lower Mississippi Riverine Forest east 862 431 1.1094732 1.5791848 -1.3579194 3.5768658 0.0000000 0.0008916 -0.0586276 0.0586276 0.8162650 0.0299873 0.4762559 1.1562741 3.2476766 1.7895158 4.705837 1.9199703 0.6244708 3.2154699 21.380379 14.228763 28.531995 0.7011640 0.2090084 1.193320
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1394 697 0.2950328 0.5338401 -1.1390113 1.7290769 0.0000000 0.0003918 -0.0388516 0.0388516 0.4294912 0.0362479 0.0558125 0.8031700 0.0000000 -498.1706832 498.170683 2.8480001 -495.1289443 500.8249444 11.237830 -54.994630 77.470290 7.8052604 -713.7421392 729.352660
255 Prairie Parkland (Subtropical) east 446 223 3.5843628 23.1069157 -5.8669828 13.0357084 0.1928428 0.0066213 0.0328523 0.3528334 0.2159275 0.3794669 -0.9952550 1.4271100 0.0000000 -2.1891289 2.189129 1.9499328 -1.0646737 4.9645393 14.890176 10.422840 19.357511 1.5711296 -0.1849767 3.327236
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5104 2552 1.1864259 0.0822486 0.6241549 1.7486969 0.0212827 0.0000335 0.0099391 0.0326263 0.4603438 0.0074558 0.2910551 0.6296325 2.1846261 1.7663702 2.602882 0.6467296 0.3302847 0.9631744 29.329397 23.698503 34.960291 1.0891726 0.4429511 1.735394
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5262 2631 0.2435508 0.0634856 -0.2504171 0.7375188 0.0000000 0.0000900 -0.0186038 0.0186038 0.8979809 0.0141519 0.6647595 1.1312023 2.6123404 1.5258535 3.698827 1.8986116 0.9204012 2.8768220 28.445897 23.345627 33.546167 1.2791762 0.5799253 1.978427
M223 Ozark Broadleaf Forest Meadow east 604 302 2.7320551 3.7168247 -1.0554053 6.5195154 0.0000000 0.0012530 -0.0695410 0.0695410 0.7404898 0.1175070 0.0670574 1.4139222 1.5517631 0.7466424 2.356884 1.1397087 0.2459018 2.0335157 31.344434 24.959377 37.729491 0.4419843 0.1730677 0.710901
M231 Ouachita Mixed Forest east 678 339 2.5055787 3.6014372 -1.2206550 6.2318123 0.1069028 NA 0.0431601 0.1706455 NA NA NA NA 1.5956826 0.7730305 2.418335 2.6173145 0.4637910 4.7708381 8.324472 7.615972 9.032971 0.1400017 0.0502173 0.229786
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 340 170 -2.3739529 1.6121586 -4.8823758 0.1344701 0.1457104 0.0031610 0.0346370 0.2567838 0.6365113 0.1024587 0.0041412 1.2688815 2.9847243 -1.0064864 6.975935 6.7846349 -2.0582015 15.6274712 41.942146 29.766217 54.118076 0.6625831 0.3129854 1.012181
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 310 155 -2.8446825 0.1601056 -3.6344194 -2.0549455 0.0643523 0.0023018 -0.0303401 0.1590448 1.0723691 0.1285439 0.3647410 1.7799972 0.0000000 -31.3299531 31.329953 4.0620236 -26.7994526 34.9234997 67.096231 35.266266 98.926195 1.3715257 -5.8266897 8.569741
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 20 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 20 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 21 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 21 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.48042203           0.092174912    0.661084855     0.29975920
## 2       pacific -0.01240958           0.006637261    0.000599451    -0.02541861
## 3          east  0.50638980           0.091915854    0.686544869     0.32623472
## 4 interior west -0.01355819           0.001907089   -0.009820292    -0.01729608

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US 0.0136258497           0.0025422716   0.0186087021
## 2       pacific 0.0007616851           0.0002938991   0.0013377272
## 3          east 0.0125574518           0.0025148518   0.0174865614
## 4 interior west 0.0003067129           0.0002286672   0.0007549007
##   95 % CI, lower
## 1   0.0086429973
## 2   0.0001856429
## 3   0.0076283422
## 4  -0.0001414749

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.649645428              0.025283449    0.699200988
## 2       pacific    0.003327294              0.001673245    0.006606854
## 3          east    0.641207061              0.025170082    0.690540421
## 4 interior west    0.005111073              0.001708809    0.008460339
##   95 % CI, lower
## 1   6.000899e-01
## 2   4.773384e-05
## 3   5.918737e-01
## 4   1.761807e-03